Question

What would be the missing values for this

Answer 1

Given:

`$x^(2) y^(8) \cdot (x^(3) y^(?))/(x y^(3))=x^(4) y^(2)`

To find:

The missing value.

Solution:

Let the missing value be m.

`$x^(2) y^(8) \cdot (x^(3) y^(m))/(x y^(3))=x^(4) y^(2)`

Using exponent rule:
`a^m \cdot a^n=a^(m+n)`

`$ (x^(2+3) y^(8+m))/(x y^(3))=x^(4) y^(2)`

`$ (x^(5) y^(8+m))/(x y^(3))=x^(4) y^(2)`

Using exponent rule:
`(a^m)/(a^n) =a^(m-n)`

`$ x^(5-1) y^(8+m-3)=x^(4) y^(2)`

`$ x^(4) y^(5+m)=x^(4) y^(2)`

Equate x terms and y terms.

`x^4=x^4` and
`y^(5+m)=y^2`

If the bases are same, then the powers are equal.

`5+m=2`

Subtract 5 from both sides.

`5+m-5=2-5`

`m=-3`

The missing value is -3.